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The asymptotic final size distribution of multitype chain-binomial epidemic processes

Part of: Special processes Markov processes

Published online by Cambridge University Press:  01 July 2016

Mikael Andersson
Mikael Andersson*
Affiliation:
Chalmers University of Technology
*
∗ Postal address: Epidemiologi, Smittskyddsinstitutet, SE-171 82, Solna, Sweden. Email address: Mikael.Andersson@mte.ki.se
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Abstract

A multitype chain-binomial epidemic process is defined for a closed finite population by sampling a simple multidimensional counting process at certain points. The final size of the epidemic is then characterized, given the counting process, as the smallest root of a non-linear system of equations. By letting the population grow, this characterization is used, in combination with a branching process approximation and a weak convergence result for the counting process, to derive the asymptotic distribution of the final size. This is done for processes with an irreducible contact structure both when the initial infection increases at the same rate as the population and when it stays fixed.

Keywords

Multitype chain-binomial epidemic processcounting processweak convergencebranching process

MSC classification

Primary: 60J99: None of the above, but in this section
Secondary: 60K40: Other physical applications of random processes 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 92D30: Epidemiology
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 1 , March 1999 , pp. 220 - 234
Copyright
Copyright © Applied Probability Trust 1999 

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